Simple Math Can Change Your Life – The Power of Compounding
- January 3, 2019
- 0
A wise man once said, “The most powerful force in the universe is the power of compound interest”. In this month’s article we will be discussing just that, The Power of Compounding.
What is the difference between simple interest and compound interest?
Simple interest is interest calculated on the initial principal amount such as on a loan, deposit, or investment. For example, you deposit $100 into a 5-year Guaranteed Investment Certificate (GIC) that pays a 3% annual simple rate of interest. Each year $3 of interest would accrue and be payable to you upon maturity in 5 years. This means a total of $15 of interest would be payable to you once the GIC matures.
$100 + $3 + $3 + $3 + $3 + $3 = $115
Compound interest is interest calculated on the initial principal amount which also includes accumulated interest over the period. More simply put, it includes “interest on the interest”. For example, you deposit $100 into an investment that pays a fixed 3% compound interest. In this case, in the first year you would receive $3 interest but in the second year you receive interest both on the original deposit amount as well as the $3 interest that accrued in the first year. In year three you would receive interest on the original deposit amount as well as on the interest accrued in the previous two years.
$100 + $3 + $3.09 + $3.18 + $3.28 + $3.38 = $115.93
As you can see from the examples above, 3% compound interest is a greater return than 3% simple interest. If we were to convert 3% simple interest into a compound interest rate it would only be equal to about 2.83% compound interest.
At this point, you are likely starting to feel like you are back in high school math class (everyone’s favourite class) learning arithmetic but it is very important to understand this simple math and the power of compounding.
What makes it so powerful?
The power of compounding is important because it has the power to change your life and give you a brighter future. The key element of compounding that makes it so powerful is ‘time’. The more time there is to compound, the more powerful it becomes. There is an exponential relationship to compounding that does not exist with simple interest. The previous examples in this article use a small $100 principal and a short period of only 5 years. But what if we increase the initial principal and extend the time horizon to give it more power?
While the simple interest in the graph above grows at a straight line, the compound interest line is getting steeper and steeper over time. This is because of the effects of compounding - “interest on the interest” – and its exponential relationship with time. At year 5 the difference is only a little more than $1,000. But by year 10 the compounded interest is almost $6,000 more. By year 25, the difference is more than $73,000!
Hopefully by now I’ve convinced you that the power of compounding is indeed a powerful force. But why should this matter to you and how can it improve your life?
Why does it matter?
With enough time many things can come to pass: wounds can heal; life can grow; goals can be met. Those from humble beginnings can become wealthy and your dreams can become your reality. The more time you allow for the possibilities to manifest the easier it will be to realize them. Something that seems modest today can become something greater in the future; if you allow it adequate time to grow
.
Take for instance the case of these identical twins on their 18^{th} birthday.
Neither is certain as to what they want their future to be; whom it will be with or what they will do. Neither twin has a high income but they both have some income. One decides to start saving for the future and starts investing $150 a month on their 18^{th} birthday while the other decides to wait
Early Saver | Late Saver | |||
Age | Saved
Monthly |
End Value | Saved
Monthly |
End Value |
18 | $150 | $1,857 | $0 | $0 |
19 | $150 | $3,844 | $0 | $0 |
20 | $150 | $5,970 | $0 | $0 |
21 | $150 | $8,245 | $0 | $0 |
22 | $150 | $10,679 | $0 | $0 |
23 | $150 | $13,284 | $0 | $0 |
24 | $150 | $16,071 | $0 | $0 |
25 | $150 | $19,053 | $0 | $0 |
26 | $150 | $22,244 | $0 | $0 |
27 | $150 | $25,658 | $0 | $0 |
28 | $0 | $27,454 | $150 | $1,857 |
29 | $0 | $29,376 | $150 | $3,844 |
30 | $0 | $31,432 | $150 | $5,970 |
31 | $0 | $33,632 | $150 | $8,245 |
32 | $0 | $35,986 | $150 | $10,679 |
33 | $0 | $38,505 | $150 | $13,284 |
34 | $0 | $41,201 | $150 | $16,071 |
35 | $0 | $44,085 | $150 | $19,053 |
36 | $0 | $47,171 | $150 | $22,244 |
37 | $0 | $50,473 | $150 | $25,658 |
38 | $0 | $54,006 | $150 | $29,311 |
39 | $0 | $57,786 | $150 | $33,220 |
40 | $0 | $61,831 | $150 | $37,402 |
41 | $0 | $66,159 | $150 | $41,877 |
42 | $0 | $70,791 | $150 | $46,666 |
43 | $0 | $75,746 | $150 | $51,789 |
44 | $0 | $81,048 | $150 | $57,272 |
45 | $0 | $86,721 | $150 | $63,138 |
46 | $0 | $92,792 | $150 | $69,414 |
47 | $0 | $99,287 | $150 | $76,130 |
48 | $0 | $106,238 | $150 | $83,317 |
49 | $0 | $113,674 | $150 | $91,006 |
50 | $0 | $121,631 | $150 | $99,233 |
51 | $0 | $130,146 | $150 | $108,037 |
52 | $0 | $139,256 | $150 | $117,456 |
53 | $0 | $149,004 | $150 | $127,535 |
54 | $0 | $159,434 | $150 | $138,320 |
55 | $0 | $170,594 | $150 | $149,859 |
56 | $0 | $182,536 | $150 | $162,206 |
57 | $0 | $195,313 | $150 | $175,418 |
58 | $0 | $208,985 | $150 | $189,554 |
59 | $0 | $223,614 | $150 | $204,680 |
60 | $0 | $239,267 | $150 | $220,865 |
61 | $0 | $256,016 | $150 | $238,182 |
62 | $0 | $273,937 | $150 | $256,712 |
63 | $0 | $293,113 | $150 | $276,539 |
64 | $0 | $313,631 | $150 | $297,754 |
65 | $0 | $335,585 | $150 | $320,454 |
another 10 years until he has a better idea of what he wants to do with his life before he starts saving. The twin who starts saving earlier only saves for 10 years due to some unforeseen circumstance and the second twin saves the same $150 every month, excluding those first 10 years, until they both retire after they turn 65 years old.
The table on the right shows what their ultimate investment results would be assuming a 7% compound rate of return over their working lives.
The twin who started saving later saved a total of $68,400. After factoring in the compounded interest, he finished with a total investment value of $320,454.
The twin that started saving earlier but stopped after 10 years only saved a total of $18,000. Miraculously, due to the power of compounding and the longer time invested, he has accumulated a total investment value of $335,585 despite saving almost a quarter as much as his identical twin.
Early Saver | Late Saver | |
Total Saved | $18,000 | $68,400 |
Final Value | $335,585 | $320,454 |
Even modest savings can grow to become something significant if given adequate time. As you can see from the example above, it can also save you a lot of money. Don’t let time pass you by or it will eventually become a headwind. Put the power of compounding to work for your benefit and let time be a tailwind to your financial destination.